1. Field of the Invention
This invention is related in general to the field of scanning interferometry and, in particular, to a novel approach for correcting motion errors in the scanning arm of an interferometer.
2. Description of the Related Art
Conventional scanning interferometry utilizes a light source, such as white light or a laser beam, to produce interference fringes at a light detector as the optical path difference (OPD) between a test surface and a reference surface is varied during a vertical scan. All measurement techniques based on phase-shifting interferometry (PSI), vertical-scanning interferometry (VSI, also referred to as white-light interferometry), and phase-shifting interferometry on-the-fly (PSIOTF) rely on an analysis of the interference between two beams of light. One beam (the object beam) is reflected from the sample; the other beam (the reference beam) is reflected from the reference mirror; and the two beams are recombined to create an interference pattern (the interferogram) at each scanning step. A detector (usually a CCD camera) registers the interferogram in a number of frames while the optical path difference (OPD) between the interfering beams is changing in a predefined fashion, which is realized either by moving the object, or by scanning the interferometric objective or the reference mirror at a preferably constant speed. The resultant shape of the sample object is calculated based on the intensity patterns in the interferograms and can be used to describe the height profile of the sample.
PSI is preferably used for measurements of smooth surfaces with small changes in profile (see K. Creath, xe2x80x9cTemporal Phase Measurement Methods,xe2x80x9d Interferogram Analysis, Institute of Physics Publishing Ltd., Bristol, 1993, pp. 94-140). VSI is generally used to measure smooth and/or rough surfaces with large interpixel height ranges (K. G. Larkin, xe2x80x9cEfficient Nonlinear Algorithm for Envelope Detection in White Light Interferometry,xe2x80x9d J. Opt. Soc. Am., A/Vol. 13, 832-843 (1996). The combination of VSI and PSI in used in the PSIOTF technique to improve measurements of smooth surfaces in the medium height range (A. Harasaki et al., xe2x80x9cImproved Vertical Scanning Interferometry,xe2x80x9d Appl. Opt. 39, 2107-2115, 2000).
In VSI the interference fringes are localized only in a small region around the focus because of the low coherence source or the high numerical aperture of the microscope objective employed. While scanning through focus, fringes for different parts of the sample surface are produced and analyzed resulting in an unambiguous measurement of the object shape. As well understood by those skilled in the art, the height information from a low-coherence interferogram can be retrieved in many ways, such as, for example, by peak detection of the coherence envelope or fringe, by calculation of the centroid of the intensity signal, or by determination of the slope of the phase of the average wavelength. All these methods of analysis estimate the best vertical-scan focus position for a given pixel by sensing the coherence peak and utilize this information to determine the relative height difference between pixels (that is, a height profile of the test surface).
In PSI techniques the interference fringes are examined only around a single focus position using typically a quasi-monochromatic light source, such as a laser. Algorithms employed to analyze PSI fringes produce phase measurements that may be ambiguous (because of so-called 2xcfx80 ambiguities) and therefore require further processing to remove the ambiguity by unwrapping the phase data. Because of this limitation, only objects with relatively small inter-pixel height differences can be measured using conventional PSI analysis. On the other hand, the advantage of PSI versus VSI techniques is that PSI allows for more precise measurements.
The PSIOTF technique affords the high precision of PSI combined with the lack of ambiguity of VSI measurements. Accordingly, this combined technique is often utilized for determining the shape of smooth surfaces with large height differences (that is, surfaces with steep profiles). The procedure first involves finding a coarse focus position for each pixel using a VSI technique; then a PSI algorithm is applied to the intensity data collected at frames around this focus position to achieve a high precision measurement where the 2xcfx80 ambiguity has already been resolved by VSI. The PSIOTF technique can be used with a low-coherence light source or with a combination of both a low- and a high-coherence source. In addition, the technique can be applied to each pixel individually or to groups of pixels in separate areas, as in the case of a stepped sample with separate smooth and flat regions.
All of these techniques require a well-calibrated and, preferably, a constant scanning motion of the sample object along the optical axis because the height calculations are based on the scanning distance traveled between interferogram frames. Scanner miscalibration, nonlinearities and vibrations affect the surface-profile measurements produced by PSI, VSI and PSIOTF algorithms by attributing an incorrect size to each scanner step. Thus, the rate of change in the OPD, normally referred to in the art as the xe2x80x9cphase step,xe2x80x9d needs to be well calibrated in order to achieve an accurate measurement. The most commonly used algorithms for the three interferometric techniques mentioned here require a predefined, nominal phase step which, once the scanner is calibrated, is assumed to remain constant along the whole scan for each measurement. However, this is not always the case and the errors in scanning speed influence the final result and need to be accounted for accurate measurements.
A common example of a source of scanning error is linear phase-step miscalibration, where the phase step is constant but different than the calibrated phase step, which may produce height magnification errors (in VSI), residual ripples (in PSI), or a saw-tooth profile (in PSIOTF). Such effects may be visible in the calculated profile. For example, FIGS. 1A and 1B show a saw-tooth effect in the phase map (x and y profiles, respectively) of a chromium-coated step height standard using a PSIOTF technique. Phase step miscalibration was present, causing saw-tooth effects following the fringes. The PSI phase calculated around each frame reflects real changes in the optical path, but the frame number position is only assumed based on the device""s calibrated phase step; therefore, a correction is needed for a precise profile measurement. Improved calibration and a feed-back loop control in the scanner system have been the conventional approaches used to reduce this source of error. FIGS. 2A,2B and 3A,3B illustrate similar scanner-error effects produced by VSI and PSI techniques, respectively.
Another example of a scanning-error source is high frequency vibrations, which introduce random errors in the intensity values of the interferograms. They may also produce a decrease of fringe contrast, residual ripples, or a saw-tooth profile in all interferometric measurement techniques. The most common way of reducing of this type of error is through better vibration isolation, such as with air tables and a more rigid structure for the instrument.
Low-frequency vibrations, miscalibration, and nonlinearity in the scanner motion result in erroneous height-difference readings, which may produce ripples, or a saw-tooth profile, or height magnification errors. In practice, these errors cannot be easily corrected. In addition, they are usually not repeatable from measurement to measurement; therefore, they are the most difficult errors to correct. Thus, eliminating or reducing the influence of these errors would be a great advance in the art.
Various studies have characterized the errors associated with scanning perturbations and improved algorithms have been developed to reduce sensitivity to these error sources, but all state-of-the-art corrective techniques require intense calculations that greatly affect processing speed. For example, U.S. Pat. No. 5,953,124 describes a technique for correcting scanning nonlinearities using the three-dimensional interferogram produced by a completed vertical scan. The phase history determined within the coherence region of each pixel during the scan is temporally unwrapped to remove 2xcfx80 ambiguities, and overlapping temporal phase histories gathered from different pixels are connected to produce a measured phase history for the entire scan range. This measured phase history is then compared to the temporal phase change nominally produced by each scanner step to correct the height profile of the test surface. The approach produces corrected results that account for scanner nonlinearities, but it requires unwrapping of the phase data and complex post-scan data manipulation. These requirements prevent utilization of the method on-the-fly and further increase time, storage, and data-processing demands.
Thus, there is still a need for a more direct and computationally fast approach to correcting the errors introduced by nonlinearities, miscalibration, or vibrations at each scanner step, so that a correct height profile can be determined on the basis of the actual, rather than the nominal, position history of the scanning mechanism. This invention provides a simple solution to this problem by focusing on the actual phase step occurring between scanning frames.
One primary objective of this invention is an improved method for measuring the actual size of each phase step between consecutive frames produced by the scanning mechanism of an interferometric profiler.
Another important goal of the invention is a method that does not require storage of the entire three-dimensional interferogram produced by a vertical scan, nor the post-scan processing of these data, to identify scanning errors due to nonlinearities or other error sources.
In particular, another goal is an approach that does not require phase calculation and unwrapping as intermediate steps to phase-step correction.
A final objective is a method that can be readily implemented in conventional interferometric profilers and that is equally suitable for correction of PSI, VSI, or PSIOTF techniques.
Therefore, according to these and other objectives, the present invention consists of performing a vertical scan of the test surface in conventional manner to produce multiple frames of interferograms corresponding to successive scanner steps; that is, a correlogram is developed for each pixel. Regardless of the technique employed for calculating the surface profile (PSI, VSI, or PSIOTF), at each frame for which sufficient intensity data are available for a pixel, the actual scan-step size between frames is calculated from the intensity data collected around the frame of interest. For example, any of several algorithms normally used for scanner calibration is suitable for determining the actual step size between successive frames captured by the scanner. Thus, a true history of actual scan-step sizes and actual frame positions can be accumulated for the entire scan, so long as sufficient overlaps of coherence regions for different pixels exist to provide continuity of data. The true scan-step sizes so measured are then used in standard PSI, VSI or PSIOTF algorithms, instead of the nominal phase step, to calculate the test surface profile.
The scan-step size can be calculated directly using a common irradiance algorithm (such as conventionally used in PSI calibration procedures) that utilize multiple-frame intensity data. According to one embodiment, the invention utilizes a five-frame algorithm that produces an average scan-step size of four scan steps around the frame of interest. This method is direct and fast because it only requires processing of five intensity values at each frame. According to another embodiment of the invention, the phase step between frames is calculated directly utilizing a novel five-frame algorithm that produces an improved approximation of the actual phase-step size at a given frame, rather than an average value of four steps around the frame. The phase step is then converted to scan-step sizes, thereby providing a frame-by-frame measure of each actual step size of the scan. Since the nominal phase step used in scanners is typically xcfx80/2, this approach does not require phase unwrapping for nearly linear scanners. Therefore, these methods require minimal data processing and can advantageously be applied xe2x80x9con-the flyxe2x80x9d as intensity data are acquired during scanning. Multiple scan steps can be calculated from any or all pixels with overlapping coherence regions and an average can be used to improve the reliability of the procedure. If coherence discontinuities exist, so that certain frames in the correlogram do not provide sufficient information to calculate the actual scan-step size, the nominal phase step can be used without correction in those regions or an average or interpolated scan-step size calculated from adjacent frames can be substituted therefor. In either case, the corrected scanner position history produces improved results over the use of calibrated, nominal phase steps utilized in the algorithms to calculate the test-surface profile.
Various other purposes and advantages of the invention will become clear from its description in the specification that follows and from the novel features particularly pointed out in the appended claims. Therefore, to the accomplishment of the objectives described above, this invention consists of the features hereinafter illustrated in the drawings, fully described in the detailed description of the preferred embodiment and particularly pointed out in the claims. However, such drawings and description disclose but one of the various ways in which the invention may be practiced.